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Thermal analysis of carbon ber polymer-matrix compositesby electrical resistance measurement
D.D.L. Chung*
Composite Materials Research Laboratory, Department of Mechanical & Aerospace Engineering,
State University of New York at Buffalo, Buffalo, NY 14260-4400, USA
Received 14 March 2000; received in revised form 14 July 2000; accepted 14 July 2000
Abstract
Thermal analysis conducted on carbon ber polymer-matrix structural composites by DC electrical resistance measurement
provided information on structural transitions, residual stress, composite interfaces, the composite fabrication process, and
thermal damage. The composites involved continuous carbon bers in single ber and laminate forms, together with
thermoplastic and thermoset matrices. The experimental methods and data interpretation are covered in this review.
# 2000 Elsevier Science B.V. All rights reserved.
Keywords: Thermal analysis; Polymer-matrix composite; Carbon ber; Electrical resistance; Electrical resistivity
1. Introduction
Thermal analysis refers to the analysis of a material
through measurement of a quantity as a function of
temperature. The quantity may be heat (as in the case
of calorimetry, usually differential scanning calorime-
try, or DSC [110]), weight (as in the case of thermo-
gravimetry, i.e., thermogravimetric analysis, or TGA
[11,12]), dimension (as in the case of dilatometry, i.e.,
thermomechanical analysis, or TMA [3,8,10]),dynamic mechanical properties such as loss tangent
and storage modulus (as in the case of dynamic
mechanical analysis, or DMA, i.e., dynamic thermo-
mechanical analysis, or DTMA [36,9,10,1216]),
etc. Thermal analysis can provide information on
structural transitions, specic heat, coefcient of ther-
mal expansion (CTE), process kinetics, thermal sta-
bility and composition.
A method of thermal analysis, which has received
relatively little attention involves measurement of the
electrical resistance as a function of temperature [17
22]. This method requires the material to be electri-
cally conducting. Thus, a polymer which is insulating
is not suitable for this method. However, polymers
containing electrically conducting llers are conduct-
ing and are thus suitable for this method. An example
of such a material is a polymer reinforced with con-
tinuous carbon bers, which are conducting and ren-der the composite high strength and high modulus, as
required for lightweight structures. This paper is a
review that uses this widely used structural composite
material to illustrate the application of thermal ana-
lysis in the form of the measurement of electrical
resistance as a function of temperature.
The measurement of electrical resistance is fast,
nondestructive and simple in terms of the equipment,
which may be portable. It is thus amenable to process
monitoring in real time, even in the eld. It provides
information on structural transitions, residual stress,
Thermochimica Acta 364 (2000) 121132
* Tel.:1-716-645-2593; fax: 1-716-645-3875.E-mail address: ddlchung@acsu.buffalo.edu (D.D.L. Chung).
0040-6031/00/$ see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 0 4 0 - 6 0 3 1 ( 0 0 ) 0 0 6 3 1 - 6
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composite interfaces, the composite fabrication pro-
cess, and thermal damage.
2. Structural transitions and thermal stress
The polymer matrix of a composite material canundergo structural transitions such as glass transition,
melting, cold-crystallization and solid-state curing.
Although the polymer matrix is insulating, the effect
of a structural transition on the ber morphology (e.g.,
the ber waviness) results in an increase in the elec-
trical resistivity of the composite in the ber direction,
thereby allowing the resistance change to indicate a
structural transition of the matrix [17,18].Due to the mismatch in the coefcient of thermal
expansion (CTE) between polymer and ber and the
fact that the composite is fabricated at an elevated
temperature, thermal stress is reduced upon heating
the composite and is increased upon cooling. The
thermal stress leads to an increase in the degree of
ber waviness or a decrease in the degree of ber
alignment, thereby increasing the resistance in the
ber direction of the composite. Thus, the electrical
resistance provides an indication of the thermal stress.
The glass transition and melting behavior of athermoplastic polymer depends on the degree of crys-
tallinity, the crystalline perfection and other factors
[2328]. Knowledge of this behavior is valuable for
the processing and use of the polymer. This behavior is
most commonly studied by DSC [2328], although theDSC technique is limited to small samples and the
associated equipment is expensive and not portable.
As the degree of crystallinity and the crystalline
perfection of a polymer depend on the prior processing
of the polymer and the effect of a process on the
microstructure depends on the size and geometry ofthe polymer specimen, it is desirable to test the actual
piece (instead of a small sample) for the glass transi-
tion and melting behavior. The measurement of elec-
trical resistance provides a technique for this purpose.
DSC is a thermal analysis technique for recording
the heat necessary to establish a zero temperature
difference between a substance and a reference mate-
rial, which are subjected to identical temperature
programs in an environment heated or cooled at a
controlled rate [29]. The recorded heat ow gives a
measure of the amount of energy absorbed or evolved
in a particular physical or chemical transformation.
The concept behind the electrical resistance technique
is totally different from that of DSC. This technique
involves measuring the DC electrical resistance whenthe polymer has been reinforced with electrically
conducting bers such as continuous carbon bers.
The resistance is in the ber direction. The polymer
molecular movements that occur at the glass transition
and melting disturb the carbon bers, which are much
more conducting than the polymer matrix, and thus
affect the electrical resistance of the composite in the
ber direction, thereby allowing the resistance change
to indicate the glass transition and melting behavior.
Exposure of polyamides to heat and oxygen may
cause changes in the physical and chemical character-istics due to thermal oxidative degradation [30] and
thus changes in the mechanical properties. Prolonged
annealing at a high temperature results in undesirable
changes in the degree of crystallization and in the end
groups, and may cause inter- and intra-molecular
transamidation reactions, chain scission and cross-
linking [3136]. The electrical resistance technique
is capable of studying the effect of annealing (in air at
various temperatures below the melting temperature
for various lengths of time) on the glass transition and
melting behavior.
2.1. DSC analysis of Nylon-6-matrix composite
Fig. 1(a) shows the DSC thermogram of the as-
received carbon ber Nylon-6-matrix composite. The
glass transition was not observed by DSC. Tm (melting
temperature, as indicated by the peak temperature)
was 218.58C. Fig. 1bf shows the effect of annealing
time and temperature on the melting peak. The DSC
results are summarized in Table 1 [17]. Since Tm and
DH of as-received and 1008C (5 h) annealed sampleswere almost the same (Fig. 1(a) and (b)), it was
attributed to the little change of the crystal perfection
or the degree of crystallinity during annealing at
1008C for 5 h. Fig. 1(c) shows the DSC thermogram
of the sample annealed at 1808C for 5 h. It reveals two
endothermic melting peaks with peak temperatures of
216 and 1958C. The lower temperature peak may be
because of the structural reorganization during anneal-
ing in which the amorphous portion partly developed
crystallinity [24,37,38]. As the annealing time
increased to 15 h (Fig. 1(d)), the high-temperature
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peak shifted to a lower temperature, but DHincreased.
As the annealing time increases to 30 h (Fig. 1(e)), the
area of the low-temperature peak increased while that
of the high-temperature peak decreased. These effects
are probably due to the reorganization and thermal
oxidative degradation of the Nylon-6 matrix, as
explained below. When the annealing time increased
from 5 (Fig. 1(c)) to 15 h (Fig. 1(d)), the degree of thecrystallinity increased, so DH increased. However, at
the same time, the extent of degradation increased due
to thermal oxidation, which occurred during annealing
at a high temperature (1808C), thus resulting in lower
crystal perfection. Therefore, the high-temperature
peak shifted to a lower temperature. When the anneal-
ing time was long enough (30 h, Fig. 1(e)), the crystal-
line portion from the reorganization process became
dominant, as indicated by the increase of the area of
the low-temperature peak. When the sample had beenannealed at 2008C for 5 h (Fig. 1(f)), both Tm and DH
decreased relative to the as-received sample. One
possible explanation is that when the annealing tem-
perature was very high, the extent of thermal degrada-
tion was extensive, resulting in less crystalline
perfection as well as a lower degree of crystallinity.
2.2. Analysis of the DC electrical resistance for the
Nylon-6-matrix composite
Fig. 2(a) [17] shows the fractional change in resis-tance for the as-received carbon ber Nylon-6-matrix
composite during heating, in which the temperature
was raised from 25 to 3508C at a rate of 0.58C/min.
Two peaks were observed. The onset temperature of
the rst peak was 808C and that of the second peak was
2208C. The rst peak is attributed to matrix molecular
movement above Tg; the second peak is attributed to
matrix molecular movement above Tm. Because the
molecular movement above Tg is less drastic than that
above Tm, the rst peak is much lower than the second
one. As indicated before, the DSC thermogram of theas-received composite does not show a clear glass
transition (Fig. 1(a)). Therefore, the resistance is more
sensitive to the glass transition than DSC. The onset
temperature (2208C) of the second peak (Fig. 2(a)) is
higher than the onset temperature (Tonset 200X9C)
of the DSC melting peak (Fig. 1(a)) and is close to the
Fig. 1. DSC thermograms showing the melting endothermic peaks
before and after annealing at the temperatures and for the timesshown: (a) as-received; (b) 1008C, 5 h; (c) 1808C, 5 h; (d) 1808C,
15 h; (e) 1808C, 30 h; (f) 2008C, 5 h.
Table 1
Calorimetry data for Nylon-6/CF composite before and after annealing
Annealing condition Tml (8C)a
Tonset (8C)b
Tm (8C)c
DH (J/g)d
Designation Temperature (8C) Time (h)
a e e 200.9 218.5 26.7
b 100 5 205.5 218.2 26.6
c 180 5 194.8 201.3 215.5 34.8
d 180 15 196.3 201.4 208.9 39.1
e 180 30 196.3 200.0 209.0 38.6
f 200 5 208.3 212.9 216.4 16.5
a Peak temperature of the low-temperature melting peak.b Onset temperature of the high-temperature melting peak.c Peak temperature of the high-temperature melting peak.d Heat of fusion.e As-received.
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Fig. 2. Effect of annealing condition on the variation of the electrical resistance with temperature: (a) as-received; (b) 1008C, 5 h; (c) 1808C,
5 h; (d) 2008C, 5 h; (e) 1808C, 15 h; (f) 1808C, 30 h.
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melting temperature (Tm 218X5C) indicated by
DSC (Fig. 1(a)). The matrix molecular movement at
Tonset is less intense than that at Tm, thereby giving no
effect on the resistance curve at Tonset. Another reasonmay be a time lag between the matrix molecular
movement and the resistance change.
Fig. 2(b)(d) shows the effect of the annealing
temperature. Comparison of Fig. 2(a) and (b) shows
that annealing at 1008C for 5 h (Fig. 2(b)) had little
effect on the glass transition and melting behavior of
the Nylon-6 matrix; this is consistent with the DSC
results (Fig. 1(a) and (b)). When the annealing tem-
perature increased to 1808C (Fig. 2(c)), the peak due to
molecular movement above Tg disappeared. This is
attributed to the increase of the degree of crystallinitydue to annealing. Because the crystalline portion has
constraint on the molecular mobility, the higher the
degree of crystallinity, the lesser is the possibility of
molecular movement above Tg.
Not only does the degree of crystallinity but also the
extent of thermal degradation affects the molecular
mobility above Tg. Fig. 2(d) shows the fractional
change in resistance of the sample annealed at
2008C for 5 h. No peak due to molecular movement
above Tg was observed. The degree of crystallinity
was less than that of the as-received sample, as shownby DH in Table 1. However, the higher extent of
thermal degradation resulted in less molecular move-
ment above Tg.
Fig. 2(c) and (e) shows the effect of annealing time
from 5 to 15 h at 1808C. The height of the peak due to
molecular movement above Tm decreased as the
annealing time increased. A longer annealing timeresulted in more thermal degradation of the matrix,
which retarded the molecular movement above Tm.
That this effect is due to a change of the extent of
thermal degradation is also supported by the effect of
annealing temperature, as shown in Fig. 2(c) and (d).
A higher annealing temperature probably enhanced
the extent of thermal degradation, thus resulting in a
decrease of the height of the peak associated with
molecular movement above Tm. Since the tail is more
pronounced for samples with a larger extent of thermal
degradation, as shown in Fig. 2(d) and (f), it may beattributed to the lower molecular mobility due to
extensive thermal degradation.
2.3. Analysis of the DC electrical resistance for the
polyphenylenesulde-matrix composite
Fig. 3 [18] shows the fractional change in resistance
of as-received carbon ber polyphenylenesulde
(PPS)-matrix composite during the rst two cycles
of thermal cycling, in which the temperature was held
at 2358C for 10 h in each cycle. The resistanceincreased abruptly during the rst heating. During
the subsequent period in which the temperature was
held at 2358C, the resistance gradually decreased to
Fig. 3. Fractional change in electrical resistance during the rst two cycles of thermal cycling for as-received composite.
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levels below the initial resistance. During subsequent
cooling, the resistance abruptly increased. During
heating in the following cycle, the resistance
decreased abruptly. The effect of cooling at the end
of the rst cycle on the resistance was reversed upon
heating at the beginning of the second cycle. In the
constant temperature (2358C) period of the secondcycle, the resistance gradually decreased, as in the rst
cycle.
Fig. 4 [18] shows the fractional change in resistance
of carbon ber PPS-matrix composite that had been
annealed at 1808C for 5 h during the rst four cycles of
thermal cycling, in which the temperature was held at
1808C for 2 h in each cycle. The resistance increased
abruptly during the rst heating, as in Fig. 3. During
the subsequent period in which the temperature was
held at 1808C, the resistance decreased to levels below
the initial resistance. During subsequent cooling, theresistance increased. In every subsequent cycle, the
resistance decreased during heating, decreased further
during holding at 1808C to levels below the minimum
resistance of the previous cycle, and increased during
subsequent cooling. As cycling progressed, the resis-
tance decrease in the 1808C constant temperature
period became more and more gradual.
Fig. 5 [18] shows the fractional change in resistance
of carbon ber PPS-matrix composite that had been
annealed at 1808C for 15 h during the rst three cycles
of thermal cycling, in which the temperature was held
at 1808C for 10 h in each cycle. The resistance
decreased abruptly during the rst heating, in contrast
to the abrupt increase in Figs. 3 and 4. Other than this,
the pattern of resistance changes in Fig. 5 is the same
as that in Figs. 3 and 4. However, the fractional
changes in resistance are smaller in Fig. 5 than in
Figs. 3 and 4.The abrupt resistance increase during the rst heat-
ing, observed only for the as-received composite and
the composite annealed at 1808C for 5 h, is attributed
to the poor bond between ber and matrix and the
resulting ow of the matrix during heating above Tg.
The ow probably led to an increase in the degree of
ber waviness or a decrease in the degree of ber
alignment, thereby resulting in an increase in the
resistance in the ber direction of the composite.
Annealing at 1808C for 15 h or more improved the
ber-matrix bond, thereby removing this effect. Thatthis effect is due to matrix ow is also supported by the
observation that ow (resistance increase) occurred at
a constant temperature of 1358C, in addition to occur-
ring during temperature increase.
The increase in resistance during cooling and
decrease in resistance during subsequent heating
(Figs. 35) are a reversible effect associated with
the build-up of the thermal stress upon cooling and
reduction of the thermal stress upon heating. The
resistance decrease during rst heating in Fig. 5 is
also attributed to reduction in thermal stress.
Fig. 4. Fractional change in electrical resistance during the rst four cycles of thermal cycling for composite annealed at 1808C for 5 h.
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The gradual decrease in resistance in the high
temperature isothermal period of each cycle
(Figs. 35) is attributed to crystallization of the matrix.
Crystallization (known as transcrystallization) occurs
on the ber surface [39], thereby tending to decrease
the ber waviness. Hence, the resistance of the com-
posite is decreased. The higher is the degree of crystal-linity of the matrix, the lower is its resistance.
Therefore, the minimum resistance of a cycle
decreased cycle by cycle (Figs. 4 and 5). On the other
hand, annealing at 1808C for 25 h (not shown) caused
the crystallinity to essentially attain its maximum, so
the above-mentioned effect due to crystallization
essentially vanished. Annealing at 1808C for 15 h
caused some crystallization (though not the maxi-
mum), so the above-mentioned effect due to crystal-
lization is smaller in Fig. 5 than Figs. 3 and 4.
3. Interlaminar interface and thermal damage
The study of the interlaminar interface is commonly
performed by measuring the interlaminar shear
strength (ILSS) by techniques such as the short-beam
method [40], the Iospiescu method [41] and other
methods [42]. Although ILSS is a valuable quantity
that describes the mechanical property of the joint
between laminae, it gives little information on the
interfacial structure, such as the extent of direct con-
tact (with essentially no polymer matrix in between)
between bers of adjacent laminae and the residual
interlaminar stress resulting from the anisotropy
between adjacent laminae. The anisotropy is severe
when the bers in the adjacent laminae are in different
directions, since the bers and polymer matrix differ
greatly in modulus and thermal expansion coefcient.Direct contact between bers of adjacent laminae
occurs due to the ow of the matrix during composite
fabrication and the waviness of the bers. Direct
contact means that the thickness of the matrix between
the adjacent bers is so small (say, a few angstrom)
that electrons can tunnel or hop from one ber to the
other. The presence of direct contact has been shown
by the fact that the volume electrical resistivity of
carbon ber epoxy-matrix composites in the through-
thickness direction is nite, even though the epoxy
matrix is electrically insulating [43].The contact electrical resistivity of the interlaminar
interface can be used as a quantity to describe the
structure of this interface [20,21]. Fig. 6 shows the
variation of the contact resistivity rc with temperature
during reheating and subsequent cooling, both at
0.158C/min, for samples cured at 0 and 0.33 MPa.
The corresponding Arrhenius plots of log contact
conductivity (inverse of contact resistivity) versus
inverse absolute temperature during heating are shown
in Fig. 7. From the slope (negative) of the Arrhenius
plot, which is quite linear (not completely linear,
Fig. 5. Fractional change in electrical resistance during the rst three cycles of thermal cycling for composite annealed at 1808C for 15 h.
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probably due to the effect of temperature on the
microstructure), the activation energy can be calcu-lated by using the equation
slope E
2X3kY (1)
where k is the Boltzmann's constant, T the absolute
temperature (in K), and Eis the activation energy. The
linearity of the Arrhenius plot means that the activa-
tion energy does not change throughout the tempera-
ture variation. This activation energy is the energy for
electron jumping from one lamina to the other. Elec-
tronic excitation across this energy enables conduction
in the through-thickness direction. This activation
phenomenon is common in the electrical conduction
of composite materials with an insulating matrix and
an electrically conducting ller (whether particles orbers). Based on volume resistivity measurement, an
activation energy in the range from 0.060 to 0.069 eV
has been previously reported for short carbon ber
polymer-matrix composites [44]. Direct measurement
of the contact resistivity is impossible for the short
ber composites.
The activation energies, thicknesses and room tem-
perature contact resistivities for samples made at
different curing pressures and composite congura-
tions are shown in Table 2. For the same composite
conguration (crossply), the higher the curing pres-
Fig. 6. Variation of contact electrical resistivity with temperature
during heating and cooling at 0.158C/min: (a) for sample made
without any curing pressure and (b) for sample made with a curing
pressure 0.33 MPa.
Fig. 7. Arrhenius plot of log contact conductivity vs. inverse
absolute temperature during heating at 0.158C/min: (a) for sample
made without any curing pressure and (b) for sample made with
curing pressure 0.33 MPa.
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sure, the smaller is the composite thickness (becauseof more epoxy being squeezed out), the lower is the
contact resisitivity, and the higher is the activation
energy. A smaller composite thickness corresponds to
a higher ber volume fraction in the composite. Dur-
ing curing and subsequent cooling, the matrix shrinks
while the carbon bers essentially do not, so a long-
itudinal compressive stress will develop in the bers.
For carbon bers, the modulus in the longitudinal
direction is much higher than that in the transverse
direction. Thus, the overall shrinkage in the long-
itudinal direction tends to be less than that in thetransverse direction. Therefore, there will be a residual
interlaminar stress in the two crossply layers in a given
direction. This stress accentuates the barrier for the
electrons to jump from one lamina to the other. The
greater the residual interlaminar stress, the higher is
the barrier, which is the activation energy. After curing
and subsequent cooling, heating will decrease the
thermal stress, due to the CTE mismatch between
bers and matrix. Both the thermal stress and the
curing stress contribute to the residual interlaminar
stress. Therefore, the higher the curing pressure, thelarger is the ber volume fraction, the greater is the
residual interlaminar stress, and the higher the activa-
tion energy, as shown in Table 2. Most of the values of
the activation energy shown in Table 2 are less than kT
(where k is the Boltzmann's constant and T is the
absolute temperature). This means that the electron
jumping from one lamina to the other occurs with
ease.
The curing pressure for the sample in the unidirec-
tional composite conguration is higher than that of
any of the crossply samples (Table 2). Consequently,
the thickness is the lowest. As a result, the bervolume fraction is the highest. However, the contact
resistivity of the unidirectional sample is the second
highest rather than being the lowest, and its activation
energy is the lowest rather than the highest. The low
activation energy is consistent with the fact that there
is no CTE or curing shrinkage mismatch between the
two unidirectional laminae and, as a result, no inter-
laminar stress between the laminae. This low value
supports the notion that the interlaminar stress is
important in affecting the activation energy. The high
contact resistivity for the unidirectional case can beexplained in the following way. In the crossply sam-
ples, the pressure during curing forces the bers of the
two laminae to press on to one another and hence
contact tightly. In the unidirectional sample, the bers
of one of the laminae just sink into the other lamina at
the junction, so pressure helps relatively little in the
contact between bers of adjacent laminae. Moreover,
in the crossply situation, every ber at the lamina
lamina interface contacts many bers of the other
lamina, while in the unidirectional situation, every
ber has little chance to contact the bers of the otherlamina. Therefore, the number of contact points
between the two laminae is less for the unidirectional
sample than the crossply samples.
By measuring the contact electrical resistance of the
interlaminar interface of a unidirectional continuous
carbon ber epoxy-matrix composite during shear, the
interlaminar shear process can be monitored in real
time [21]. The resistance increases throughout the
shear process for a low curing pressure, but decreases
in the initial stage of shear for a high curing pressure.
The resistance increase is due to delamination and
Table 2
Activation energy for various compositesa
Composite
configuration
Curing
pressure(MPa)
Composite
thickness(mm)
Contact
resistivityrco (O cm
2)
Activation energy (eV)
Heating at 0.158C/min Heating at 18C/min Cooling at 0.158C/min
Crossply 0 0.36 0.73 0X0131 2 105 0X0129 3 105 0X0125 8 1060.062 0.32 0.14 0X0131 4 105 0X0127 7 105 0X0127 4 105
0.013 0.31 0.18 0X0168 3 105 0X0163 4 105 0X0161 2 1050.19 0.29 0.054 0X0222 3 105 0X0223 3 105 0X0221 1 105
0.33 0.26 0.0040 0X118 4 104 0X129 8 104 0X117 3 104Unidirectional 0.42 0.23 0.29 0X0106 3 105 0X0085 4 105 0X0081 2 105
a The standard deviations are shown in parentheses.
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strain in the interface region during shear. The resis-
tance decrease observed for a high curing pressure is
believed to be due to interlaminar rubbing and slight
damage of the matrix between the ber layers and theconsequent increase in the number of contacts
between bers of the adjacent laminae. The interla-
minar displacement is negligible prior to shear failure.
The contact electrical resistivity of the interlaminar
interface can be used to monitor thermal damage in a
continuous carbon ber epoxy-matrix composite in
real time during thermal cycling [22]. The resistivity
increases in spikes and its baseline shifts due to
thermal damage.
4. Composite fabrication process
Continuous ber polymer-matrix composites with
thermosetting matrices are important structural mate-
rials due to their high strength, high modulus and low
density. These composites are commonly made by
stacking up layers of ber prepreg and subsequent
consolidation and curing under heat and pressure.
Consolidation involves the use of pressure to bring
the ber layers closer to one another and the use of
heat to melt the resin in the prepreg, so that the resinow will allow the layers to come even closer together.
A fraction of the resin may be squeezed out during
consolidation. Curing occurs subsequent to consolida-
tion and involves the resin completing its polymeriza-
tion reaction so that it sets. Curing requires sufcienttime and temperature in addition to the recommended
pressure for curing. There has been much work on
the curing process [4550], but little or no work on
the consolidation process. As consolidation is an
important step in the composite fabrication process,
understanding of the consolidation process and char-acterization of the effectiveness of consolidation are
valuable.
During consolidation, the thickness of the prepreg
stack decreases. However, thickness change does not
provide information on the extent of interaction
between the prepreg layers. In the case of the bers
being carbon bers, which are electrically conducting,
the interaction between the prepreg layers leads to
contact between bers of adjacent layers, thereby
causing the volume electrical resistivity in the
through-thickness direction (direction perpendicular
to the plane of the layers) to decrease. Hence, the
resistivity provides information on the extent of ber
ber contact. In [19] this resistivity was measured
during consolidation for the purpose of studying theconsolidation process in detail. Measurement of the
resistivity requires measurement of the resistance as
well as the thickness.
The through-thickness resistance (R) together with
the sample thickness (d) gives the through-thickness
resistivity (r) according to the equation
r RA
dY (2)
where A is the area of the sample in the plane of the
laminate. This area was assumed to be constant duringconsolidation and curing.
Let the total through-thickness resistance at a cer-
tain time during consolidation be R and that at the start
of consolidation be R0. Let the average resistance of
each through-thickness conduction path be Ri. Since
the various through-thickness conduction paths are
electrically equivalent to resistors in parallel, the total
resistance R is given by
R Ri
N
X (3)
At the start of consolidation, the resistance is
R0 Ri
N0X (4)
The change in resistance during consolidation is given
by
DR R R0 Ri
N
Ri
N0X (5)
Thus
DR
R0
N0
N 1 (6)
or
N
N0
R0
DR R0X (7)
Hence, N/N0 can be calculated from R0 and DR, which
was measured during consolidation, using Eq. (7).
Fig. 8 shows the variation of the through-thickness
electrical resistivity and N/N0 during consolidation at
a pressure of 0.56 MPa. During consolidation, the
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temperature was raised linearly and reached 1208C,
which was the curing temperature. In Fig. 8, the
resistivity decreased and N/N0 increased during con-
solidation, such that the N/N0 curve revealed three
stages of consolidation. The rst stage was character-
ized by a very gradual increase in N/N0 (due to thesolid form of the resin); the second stage was char-
acterized by an abrupt increase in N/N0 (due to the
molten form of the resin); the third stage was char-
acterized by a moderately gradual increase in N/N0(due to the thickening of the resin as the temperature
increased). Similar changes in curvature of the N/N0plot were observed for consolidation conducted at
ramped temperatures that reached 100, 110, 120,
130 or 1408C, although only the results for a max-
imum temperature of 1208C are shown in Fig. 8.
Similar effects were also observed at a pressure of1.10 MPa. The curve of N/N0 vs. temperature was
quantitatively quite independent of the maximum
temperature of consolidation, but was quantitatively
different for the two pressures. At the higher pressure,
(i) N/N0 reached much higher values, (ii) the second
stage began and ended at higher temperatures, and (iii)
the slope of the N/N0 vs. temperature curve in the
second stage was higher (7.188C1 for 1.10 MPa and
3.318C1 for 0.56 MPa). This means that pressure
hastened consolidation and promoted the extent of
consolidation, as expressed by the quantity N/N0. In
contrast, increasing the maximum temperature did not
promote the extent of consolidation.
5. Residual stress in ber embedded in matrix
Due to the shrinkage of the matrix during compositefabrication and/or the thermal contraction mismatch
between ber and matrix during cooling near the end
of composite fabrication, the bers in a composite can
have a residual compressive stress [51]. This stress
may affect the structure of the ber so that the ber
properties are affected often adversely. It may also
cause ber waviness, which degrades the mechanical
properties of the composite.
The measurement of the ber residual strain by X-
ray diffraction, Raman scattering and other optical
techniques is difcult due to the anisotropy of the berstrain and the necessity of embedding the ber in the
matrix. To help alleviate this problem, a method which
involves simultaneous electrical and mechanical mea-
surements on the same sample under load has been
developed [52]. This method is in contrast to the
separate electrical and mechanical measurements.
6. Conclusion
Thermal analysis in the form of the measurement of
DC electrical resistance, as conducted on continuous
Fig. 8. Variations ofN/N0 (solid line) and through-thickness electrical resistivity (dashed line) with temperature during consolidation heating
to 1208C at a pressure of 0.56 MPa.
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carbon ber polymer-matrix structural composites,
revealed information on the structural transitions,
residual stress, composite interfaces, the composite
fabrication process, and thermal damage. The techni-que was enabled by the electrical conductivity of
carbon bers.
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